Final answer:
In the given scenario, the angle between the transversal l and the parallel line AB is equal to the angle between the transversal l and the parallel line CD, due to the equality of interior angles on the same side of the transversal in case of parallel lines. This is a result of Euclidean geometry principles.
Step-by-step explanation:
In the scenario described, Lines AB and CD are parallel, and intersected by a transversal line, denoted as l. When two parallel lines are intersected by a transversal, corresponding angles and alternate interior angles are congruent (equal). This means that the interior angles on the same side of the transversal are equal.
If the interior angles on the same side of the transversal are equal, this implies that those angles are supplementary, which means they add up to 180 degrees. Let's suppose that the angle between line l and line CD is θ, then the angle between line l and line AB is also θ, since the interior angles on the same side of the transversal are equal.
Therefore, the angle between the transversal l and the parallel line AB is θ. This is a consequence of the Parallel Lines and Transversal properties, one of the basic postulates of Euclidean geometry.
Learn more about Parallel Lines and Transversal